Estimates of Serial Interval and Reproduction Number of Sudan Virus, Uganda, August–November 2022

We estimated the mean serial interval for Sudan virus in Uganda to be 11.7 days (95 CI% 8.2–15.8 days). Estimates for the 2022 outbreak indicate a mean basic reproduction number of 2.4–2.7 (95% CI 1.7–3.5). Estimated net reproduction numbers across districts suggest a marked spatial heterogeneity.


Serial interval
The serial interval is defined as the difference between the date of symptom onset of a case and those of his secondary cases. We estimated the serial interval distribution of Sudan Virus (SUDV) using two different datasets: • previously published data on SUDV transmission chains from the 2000-2001 outbreak in Uganda (1); • data reported by the Ministry of Health of Uganda on the transmission chains generated by one case in the 2022 SUDV outbreak in Uganda (2).
For each dataset, we considered observed serial intervals from infector-infectee pairs for which the symptom onset date was known (24 infector-infectee pairs from (1); 12 infectorinfectee pairs from (2)) and we fitted three families of distributions to the data (Weibull, Gamma, log-normal) allowing for an offset to reproduce the observation that no serial interval was below 4 and 2 days respectively in the considered data (1,2).
For both datasets, the best fitting distribution according to maximum likelihood, Akaike Information Criterion and Bayesian information Criterion was the Weibull distribution (Appendix Table 1).
The resulting estimates of the parameters of the two Weibull distributions of the serial intervals are reported in Appendix Table 2. The best-fitting cumulative density functions estimated for the serial intervals are shown in Appendix Figure 1 along with the cumulative distribution of observed serial intervals from the two datasets.
For the computation of the net reproduction number Rt and the basic reproduction number R0, we assume that the distribution of the generation time (i.e., the difference between the date of infection of a case and those of his secondary cases) can be approximated by the distribution of the serial interval.

Basic reproduction number R0 and net reproduction number Rt
The basic reproduction number R0 is defined as the average number of secondary infections generated by an infectious individual in a fully susceptible population. R0 is a key epidemiologic parameter characterizing the transmission potential of an infectious pathogen in the early epidemic phase. If R0 <1, transmission is expected to fade out even in absence of control, whereas if R0 >1, the epidemic has the potential to continue; the larger R0, the more difficult it is to control the epidemic.
During outbreaks, the transmissibility of an infectious pathogen may vary, e.g., because Different methods have been proposed in the literature to estimate the net reproduction number Rt from case incidence data (3)(4)(5). In this study, we estimate the distribution of the net reproduction number Rt at the national and district level by applying the statistical method of Where: • P(k; λ) is the probability mass function of a Poisson distribution (i.e., the probability of observing k events if these events occur with rate λ).
• C(t) is the daily number of new cases having symptom onset at time t; • Rt is the net reproduction number at time t to be estimated; • φ(s) is the integral of the probability density function of the generation time evaluated between day s-1 and s; we considered the distribution of the serial interval estimated above as an approximation of the distribution of the generation time.
We considered only the case with earliest symptom onset as imported case.
For comparison, we also computed estimates of Rt using the method proposed by Parag (5).
To estimate the basic reproduction number, in the main analysis, we use the method for We also consider alternative methods to estimate the basic reproduction number R0. If the cumulative case incidence in the early phase of the epidemic is assumed to grow exponentially, R0 can be estimated by fitting the exponential growth rate r (6,7). If the growth of cumulative cases is sub-exponential, a generalized-growth model may be more appropriate where the growth rate r is estimated in combination with an additional parameter p representing the deceleration of growth (8,9).
We provide estimates of R0 for the Mubende district from both approaches estimating their parameters through nonlinear least-square fitting to the cumulative case incidence in the first 36 days (about three generations of cases), from August 18 to September 22, 2022.

Estimates of Rt considering the 2022 serial interval
We report hereafter estimates of the net reproduction numbers over time as obtained by assuming the 2022 serial interval (2) (blue lines in Figure 1  Estimates of Rt and R0 are obtained using the serial interval as a proxy of the generation time. Given the relationship of direct proportionality existing between the reproduction number and the generation time (6,7), estimates of the reproduction numbers obtained using the 2000-2001 serial interval (mean: 12 days) are slightly higher than those obtained using the 2022 serial interval (mean: 11.7 days).

Estimates of Rt obtained using the Epifilter method
Finally, we estimated Rt for the district of Mubende using the method proposed in (5) (R implementation of EpiFilter available at https://github.com/kpzoo/ EpiFilter). We applied Epifilter assuming a uniform prior distribution for Rt over a grid of size m = 1000, defined between Rmin = 0.01 and Rmax = 10, and a state noise parameter = 0.1. Except for the first 10 days, when the cumulative number of observed cases was still very low (6), the 95% CI of our estimates always intersect with the 95% CI of estimates obtained through this alternative method (Appendix Figure 3).